A resistor and an inductor are connected in series across an AC power supply . The value of current drawn from the source is 2 A . Calculate the net impedance of circuit if voltage across inductor and resistor are 100 V and 80 V respectively.

Answer

To solve the problem, we need to calculate the net impedance of a circuit consisting of a resistor and an inductor connected in series across an AC power supply. Given the current drawn from the source is 2 A, the voltage across the inductor is 100 V, and the voltage across the resistor is 80 V, we can follow these steps:

### Step 1: Identify the given values
- Current (I) = 2 A
- Voltage across the resistor (VR) = 80 V
- Voltage across the inductor (VL) = 100 V

### Step 2: Calculate the resistance (R)
Using Ohm's law, we can find the resistance using the voltage across the resistor:
\[ R = \frac{V_R}{I} \]
Substituting the known values:
\[ R = \frac{80 \, \text{V}}{2 \, \text{A}} = 40 \, \Omega \]

### Step 3: Calculate the inductive reactance (XL)
Similarly, we can find the inductive reactance using the voltage across the inductor:
\[ X_L = \frac{V_L}{I} \]
Substituting the known values:
\[ X_L = \frac{100 \, \text{V}}{2 \, \text{A}} = 50 \, \Omega \]

### Step 4: Calculate the net impedance (Z)
In a series RL circuit, the impedance can be calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
Substituting the values we found:
\[ Z = \sqrt{(40 \, \Omega)^2 + (50 \, \Omega)^2} \]
Calculating the squares:
\[ Z = \sqrt{1600 + 2500} = \sqrt{4100} \]
Calculating the square root:
\[ Z \approx 64.03 \, \Omega \]

### Final Answer
The net impedance of the circuit is approximately \( 64.03 \, \Omega \).

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